Answer:
[tex]\boxed {\boxed {\sf 2.1 \ kilograms}}[/tex]
Explanation:
Kinetic energy is the energy an object possesses due to motion. The formula 1/2 the product of mass and the squared velocity.
[tex]E_k=\frac{1}{2} mv^2[/tex]
We know the baseball's kinetic energy is 105 Joules. It is also traveling at a velocity of 10 meters per second. `
First, convert the units of Joules to make unit cancellation easier later in the problem. 1 Joule (J) is equal to 1 kilogram square meter per square second (kg*m²/s²). The baseball's kinetic energy of 105 J is equal to 105 kg*m²/s².
Now we know 2 values:
Substitute these values into the formula.
[tex]105 \ kg*m^2/s^2= \frac{1}{2} m (10 \ m/s)^2[/tex]
Now we need to solve for m, the mass. Solve the exponent.
[tex]105 \ kg *m^2/s^2 = \frac{1}{2} m (100 \ m^2/s^2)[/tex]
Multiply on the right side.
[tex]105 \ kg *m^2/s^2 = m (\frac{1}{2} * 100 \ m^2/s^2)[/tex]
[tex]105 \ kg *m^2/s^2 = m (50 \ m^2/s^2)[/tex]
The variable, m, is being multiplied by 50 square meters per square second. The opposite of multiplication is division, so we divide both sides by that value.
[tex]\frac {105 \ kg *m^2/s^2 }{50 \ m^2/s^2}= \frac{ m (50 \ m^2/s^2)}{50 \ m^2/s^2}[/tex]
[tex]\frac {105 \ kg *m^2/s^2 }{50 \ m^2/s^2}= m[/tex]
The units of square meter per square second will cancel out.
[tex]\frac {105 }{50} \ kg= m[/tex]
[tex]2.1 \ kg=m[/tex]
The mass of the baseball is 2.1 kilograms.
